A Twitter handle associated with Mr Fayulu tweeted that the peace and stability of the DRC and the region depended on the truth being revealed through a recount.
At a summit in Addis Ababa, AU leaders announced late Thursday that they would dispatch envoys to Kinshasa in a bid to end the crisis.
According to official results announced by the Independent National Electoral Commission (CENI), opposition leader Felix Tshisekedi won the race with a 38.57% win in December's vote. The meeting that produced the announcement was chaired by Rwandan President Paul Kagame and included Uganda's Yoweri Museveni, Chad's Idriss Déby and the Congo Republic's Denis Sassou-Nguesso.
Fayulu, a former Exxon Mobil manager, says Tshisekedi, who is the president of Congo's largest opposition party, struck a deal with outgoing President Joseph Kabila to be declared victor.
The Congolese government has shut down Internet connections and text messaging services across the country for three weeks - since the day after the election - ostensibly to prevent the sharing of fake results.
Government spokesperson Lambert Mende has accused the global media of leaking information to influence the courts.
"We call upon the worldwide community to respect.the ongoing internal legal and political processes for the finalisation of the electoral process", SADC said in a statement.
The AU on Thursday criticised Congo's handling of the vote, saying it had "serious doubts" about the veracity of the outcome.
The court's ruling, and the announcement of the final results, have to be completed by next Tuesday when the new president is scheduled to be sworn in.
Sources say that South Africa and Zambia backtracked on the initial position that SADC had taken on January 13, on the grounds that a recount could heighten political tensions in DRC. The court is expected to make its ruling in the coming days.
"The Heads of State and Government attending the meeting concluded that there were serious doubts on the conformity of the provisional results, as proclaimed by the National Independent Electoral Commission, with the votes cast".
"It depends on how upset the DRC authorities are". The AU statement came hours after the 16-nation Southern African Development Community backed off its earlier demand for an election recount, instead urging the worldwide community to respect Congo's sovereignty. The African Union's statement appears to be timed to put pressure on the court and to suggest it delay its decision.
"I ask the entire global community not to recognise a power that has neither legitimacy nor legal standing to represent the Congolese people", he said of Tshisekedi, declaring himself "the only legitimate president".
Accompanied by his wife and his lawyers, Congo opposition candidate Martin Fayulu, right, petitions the constitutional court following his loss in the presidential elections in Kinshasa, Congo, on January 12, 2019.
"We consider the Constitutional Court to be our country's highest judicial institution", Vidiye Tshimanga, a spokesman for Mr Tshisekedi, said by phone.